Each synchronous machine \(i\) 
can be described [1]}, [2]} by its mechanical phase
\(\theta _i = \Omega t + \phi _i\) ,
where \(\Omega \)  is the angular frequency (\(2 \pi \cdot 50\)  or
\(2 \pi \cdot 60\)  rad s\(^{-1}\) ) and \(\phi _i\)  the phase
deviation. Note that the mechanical phase deviation \(\phi _i\)  is the same
as the electrical angle \(\delta _\)  except for a constant
factor, namely the number of poles \(n_{\rm {P}}\)  of the synchronous
machine [3]}: \(\delta _= (n_{\rm {P}}/2) \phi _i\) .
To derive the equation of motion for \(\phi _i\) , one needs to consider
energy (or power) conservation [1]}, [2]}, so that for
each synchronous machine \(i\)
\(P_i^{\rm source} = P_i^{\rm diss} + P_i^{\rm acc} + P_i^{\rm flow},\) 
